18.755 Lie groups and Lie algebras II

David Vogan, 2-355

dav@math.mit.edu

Telephone x3-4991

Office hours Monday 4:00-5:00 and Tuesday 2:30-3:30 (or any time).

Problem sets will be posted here. Grading from March 15 will be on Gradescope, accessible at GRADESCOPE. Registered students should already be on the class roster, with your Registrar name and MIT email address. If you have difficulty accessing this, let me know. PDF files of your solutions (which can be made from a photo of handwritten solutions if necessary) should be submitted on Gradescope by 16:00 Eastern Time on the due date (usually a Wednesday). The grader will mark the pdf files. Usually I hope to post solutions immediately after class Wednesday. This is the reason for the submission deadline. No extensions and no exceptions. The grading for the course will emphasize your best work, so missing one problem set should not have a serious effect. (In light of the emergency P/No Record grading, you would need to miss quite a few problem sets to have difficulty.)

For Problem Set 5, the grader has everything that was submitted by March 11. I will put on Gradescope files emailed to me after that date; but if _you_ can submit them to Gradescope, that will be very helpful.


First problem set due in class Wednesday, February 12.
First problem set solutions, to be posted after class 2/12.


Second problem set due in class Wednesday, February 19.
Second problem set solutions, to be posted after class 2/19.


Third problem set due Wednesday, February 26.
Third problem set solutions, to be posted after class 2/26.


Fourth problem set due Wednesday, March 4.
Fourth problem set solutions.


Fifth problem set due Friday, March 20 (nine day extension).
Fifth problem set solutions, to be posted Friday evening 3/20.


Sixth problem set CANCELED.


Seventh problem set due Wednesday, April 1. (An problem set from an old course was inadvertently posted here until 3/17/20. That is not the actual Problem set Seven, which should be posted by March 20.
Seventh problem set solutions, to be posted after class 4/1.


Eighth problem set due Wednesday, April 8.
Eighth problem set solutions, to be posted after class 4/8.


Ninth problem set due Wednesday, April 15.
Ninth problem set solutions, to be posted after class 4/15.


Tenth problem set due Wednesday, April 22.
Tenth problem set solutions, to be posted after class 4/22.


Eleventh problem set due Wednesday, April 29.
Eleventh problem set solutions, to be posted after class 4/29.


Twelfth problem set due Wednesday, May 6.

Twelfth problem set solutions, to be posted after class 5/6.

Relevant to class and to Problem Set 10 is notes on Weyl and Clifford algebras. I will be very grateful for corrections or suggestions about improvements.

Here is a set of notes on root systems, related to Chapter 7 of the text. This provides additional details on material I'll discuss in class at the end of the semester.

The notes that follow are older and not (so far) related to the 2015 course. Here are notes on compact classical groups.

Notes about actions of a Lie group on a manifold. You should also remember that the group SL(2,R) by its definition acts on the two-dimensional vector space R^2. Is there a way to get out of that an action on a circle?

Notes about quaternionic matrix groups. Goal is to relate quaternionic groups to complex groups. Edited Wednesday afternoon 11/5/14 to remove almost all coordinates.